Thank you, It could be just dirty MagSafe connection. Could you publish the battery conditions from About this Mac. Your Mac should be able to run without battery, but it does not indicating bad charger, bad connection or failure in logic board.
– RuskesMar 1 at 17:12

@Ruskes no, it won’t power up... except displaying the battery icon indicating it should be connected to power
– Ionică BizăuMar 2 at 19:57